Worked Example 1
Triangle ABC has sides 4, 6, 8 cm. Triangle PQR is similar, with PQ = 10 cm matching AB = 4 cm. Find QR and RP.
Step 1: find the scale factorDivide a matching pair: 10 ÷ 4 = 2.5.
Step 2: apply it to the othersQR = 6 × 2.5 = 15 cm. RP = 8 × 2.5 = 20 cm.
Step 3: checkDivide each new side by its old one: 10/4, 15/6 and 20/8 all give 2.5.
Worked Example 2
Measure a flagpole without climbing it
What you measureStand a 1.5 m stick upright in the sun. Its shadow is 90 cm. At the same moment the flagpole shadow is 4.2 m.
Why the triangles are similarBoth stand at 90° to the ground, and the sun rays hit both at the same angle.
WorkingScale factor = 4.2 ÷ 0.9 = 4.666... So the pole = 1.5 × 4.666... = 7 m.
The mistake to avoidMixing metres and centimetres. Convert first, then calculate.